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FluidPhase~qquilibria,40 (1988) 113-125 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands 113 VAPOR PRESSURES OF N-BUTANE, DIMETHYLETHER,METHYL CHLORIDE,METHANOLAND THE VAPOR-LIPUID EQUILIBRIUM OF DIMETHYLETHER - METHANOL: EXPERIMENTAL APPARATUS, RESULTSAND DATA REDUCTIDN H. HOLLOORFF and H. KNAPP Institute of Thermodynamics and Plant Design, Technical University Berlin (F.R.G.1 (Received July 27, 198’7; accepted in final form November 30, 1987) ABSTRACT Holldorff, H.andKnapp, H., 1988. Vapor pressures of n-butane, dimethyl ether, methyl chloride, meth- anol and the vapor-liquid equilibrium of dimethyl ether-methanol; experimental apparatus, results and data reduction. Fluid Phase Equilibria, 40: 113-125. A static equilibrium apparatus for experimental investigations of vapor- liquidand vapor-liquid-liquid phase equilibria at pressures10 kPa < p < 1 MPa and temperatures 250 K < T < 350 K was designedand built. The vapor pressureof n-butane was measured at 258 K < T < 357 K in order to test the the operability and accuracyof the entire system. Vapor pressures of dimethyl ether, methyl chloride and methanol were measured;Vapor-liquid equilibria in the binary mixture of dimethylether and methanolwere investigated. The experimental resultswere reduced. INTRODUCTION The design, selection, or optimization of separation processesin chemical production plants requires information on phase equilibria. In many cases It 1s not possible to predict the conditions in multicomponent and multiphase systems with sufficient accuracyand certainty. Our knowledge in molecular theory and our models of liquid solutions are still imperfect particularly for strongly interacting, highly polar or assoclatlng molecules. The required informatlon must be obtained in the experiment. Experimental data are costly and only sporadic but are essential for responsible process design and for further improvement of theory. 037%3812/88/$03.50 0 1988 Elsevier Science Publishers B.W.
Transcript
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FluidPhase~qquilibria,40 (1988) 113-125 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

113

VAPOR PRESSURES OF N-BUTANE, DIMETHYL ETHER, METHYL CHLORIDE, METHANOL AND THE

VAPOR-LIPUID EQUILIBRIUM OF DIMETHYL ETHER - METHANOL:

EXPERIMENTAL APPARATUS, RESULTS AND DATA REDUCTIDN

H. HOLLOORFF and H. KNAPP

Institute of Thermodynamics and Plant Design,

Technical University Berlin (F.R.G.1

(Received July 27, 198’7; accepted in final form November 30, 1987)

ABSTRACT

Holldorff, H. and Knapp, H., 1988. Vapor pressures of n-butane, dimethyl ether, methyl chloride, meth- anol and the vapor-liquid equilibrium of dimethyl ether-methanol; experimental apparatus, results and data reduction. Fluid Phase Equilibria, 40: 113-125.

A static equilibrium apparatus for experimental investigations of vapor-

liquid and vapor-liquid-liquid phase equilibria at pressures 10 kPa < p < 1 MPa

and temperatures 250 K < T < 350 K was designed and built.

The vapor pressure of n-butane was measured at 258 K < T < 357 K in order to

test the the operability and accuracy of the entire system.

Vapor pressures of dimethyl ether, methyl chloride and methanol were measured; Vapor-liquid equilibria in the binary mixture of dimethyl ether and methanol were investigated. The experimental results were reduced.

INTRODUCTION

The design, selection, or optimization of separation processes in chemical production plants requires information on phase equilibria. In many cases It 1s not possible to predict the conditions in multicomponent and multiphase systems with sufficient accuracy and certainty. Our knowledge in molecular theory and

our models of liquid solutions are still imperfect particularly for strongly interacting, highly polar or assoclatlng molecules.

The required informatlon must be obtained in the experiment. Experimental

data are costly and only sporadic but are essential for responsible process

design and for further improvement of theory.

037%3812/88/$03.50 0 1988 Elsevier Science Publishers B.W.

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114

This report is the first of a series of reports on results of an experimental

study of phase equilibria of mixtures containing CHJOCH3, CH,Cl, CH>OH and HZ0

(see Table 1). These components can be found for example, in plants producing methyl ceilulose and must be separated for varies reasons, such as recovery and waste water treatment.

TABLE 1

Experimental program

Substance pLv/kPa 1 2 min max

%"bO 128 1073

CH,Cl 124 1098

CH,OH 13 243

%"6O CH,OH 35 1078

TLV/K Pts min max

254 321 19

25& 322 29

293 362 15

2% 353 72

EXPERIMENTAL METHOD

At high vapor pressures, with components of very different volatilities, in

the presence of two liquid phases it is difficult to take representative liquid

samples for chemical analysis. It is advantaqous to use a static cell and

prepare the mixture gravimetrically or volumetrically. The static method is one

of the oldest methods used to study phase equilibria (Magnus 1836). Recent years

have shown an increasinq interest in this method, and a variety of apparatuses

have been described in literature (e.g. Van Ness and Gibbs 1972, Pemberton and Mash 1978, Aim 1978, Kolbe and Gmehling 1985).

EXPERIMENTAL EQUIPMENT

The static equilibrium cell is shown in figure 1. It is designed for maximum

pressures of 1.5 MPa. The cell is made of a thick-walled (9 nnn) Doran glass

cylinder (H = 100 mm, Di = 81 mn. V = 512 cm') (1) closed on both sides by

stainless steel (W 1.4571) cover-plates (2, 3) with Teflon as gasket material

(4). The cell is filled 9/10 with liquid. Corrections of the liquid composition due to partial vaporization are therefore minimal. However there is still a

vapor inventory large enough to allow withdrawal of samples without affecting

pressure and composition.

An excentric hollow-shaft stirrer (5) sucks vapor and liquid from the surface

and distributes them near the bottom. The stirrer shaft is sealed by a teflon -1 packing (6) and mercury (7) and is driven by an electric motor at 200 min .

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115

Fig. 1. Equilibrium cell

The Liquid components are injected into the cell through

are inserted through teflon-coated septa (8). The temperature

in a therm0 well (9).

The complete system is shown schematrcally in Figure 2.

capillaries, which

sensor 1s inserted

The glass equilibrium cell (1) is immersed in a double wall glass vessel (2)

containrng 40 1 of a water-glycol mixture, temperature controlled within ~0.02 K

by a circulation thermostat (3) (Haake F3-k). The thermostat has an operating

range of 250 K < T < 360 K. The cell can be viewed through a window (4). The

interspace 1s purged with dry nitrogen to prevent fogging at low operating

temperatures. Different methods are used to fill substances into the cell: low

volatile liquids (HzO, CH,OH) are carefully degassed and then transferred from

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116

Fig. 2. Schematic diagram of the static phase equilrbrium apparatus.

storage flasks (6) by diaphragm type dosrmetric pumps (5). High volatile

substances (CZH6U, CH,Cl) are distilled From the high pressure flasks (7) into

the refrrgerated cell. Liquid samples can be withdrawn through caprllaries (81,

evaporated in needle valves (VI and collected as vapor in sample flasks. The

entire system can be evacuated by a vacuum pump (15).

Instrumentation and control

The temperatures in the bath and equilibrium cell are measured by PtlOO

temperature sensors (101 in combination with a digrtal indicator (Systemteknik

51223). The system was calrbrated against a standard resistance thermometer

(Rosemount 162 CE).

The cell is connected to one side of a differential pressure gauge (Hdttxrger

Baldwin PDl/O.l) (11) whrch is located directly above the cell and heated to

9B°C to prevent condensation and to thermostat the inductive PD-transmitter. The

differential pressure indicator-controller c&p 210 kPa) is used to adjust the

reference pressure by adding or venting nitrogen (121. The reference pressure is

read on an aneroid precision pressure indicator (13) (Wallace & Tiernan 61-1500)

or set by a pressure balance (14) (Oesgranqes 6 Huot 3030-Zl-PR).

The mass of each component filled into the cell is determined gravrmetrically

on a precls~on scale (m 21 mg) by weighing the storage flasks (6 and 7) before

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117

and after filling. The composrtion of the liquid phase can be calculated after

correcting for the portlon contained in the vapor fraction.

The vapor composition can be determined by a gaschromatograph (Hewlett

Packard 5830 A) with a thermal conductivity detector calibrated with reference

mixtures.

Table 2 lists the sensitivity of the instruments or systems and their

estimated inaccuracy, resulting from calibration, fluctuation, handling, etc..

TABLE 2

Sensitivity and inaccuracy of the instrumentation

Variable Instrument or Method Sensitivity Inaccuracy

T (K) resistance thermometer 0.01 0.04

Ap (kPa1 differential pressure gauge 0.01 0.05

p (kPal aneroid manometer 0.02 0.06

p (kPa) pressure balance 0.01: 0.1%

x (mol/molj gravimetrical 0.00001 0.0001

y (mol/mol) gaschromatograph 0.00001 0.003~0.01’

* dependent on component and concentration range

SUBSTANCES

The water used is deionised and double distilled. Methanol was supplied by

Merck with a purity of min. 99.5% and a maximum water content less than 0.01%.

The inert gases were removed from both liqurds by partial evaporatian under

vacuum for 15-30 minutes.

Dimethyl ether and methyl chloride were provided by Henkel KGaA. Methyl

chloride showed no measurable impurities in gaschromatographic analysis on

Porapak Q and Carbowax 1540 columns except N2. It was degassed by repeated

freezing, evacuating the gas phase, and thawing.

Several impurities. mainly COz, were detected by gaschromatographic analysis

of the dimethyl ether. They were removed by distlllatlon. The degasslng

procedure was the same as used for methyl chloride. The final purity was

estimated to be 99.8%.

N-butane was chosen as a test substance. According to the suppliers

specifications, the purity was better than 99.95%

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118

EXPERIMENTAL RESULTS

Test measurement

The vapor pressure curve of n-butane was measured, to check the functioning

of the complete system and the accuracy of the instrumentation. The results are

shown in Table 3. The Antoine and Frost-Kalkwarf parameters are presented in

Table 5. The scattering of the experimental points can be seen in Figure 3, as

well as the deviations to vapor pressure equations recommended by other authors.

s 0.60

255 270 280 290 300 320 340 360

temperature T . K

fig. 3. Relative pressure deviation of measured data l and

different authors (OHaynes and Goodwin, 1982;v Kratzke et

al., 1977; 0 Boublik et al., 1973) compared to the vapor

(Eq. 21 of n-butane.

TABLE 3

Vapor pressure data of n-Butane

calculated values af

al., 1982;O Reid et

pressure correlation

T (K) p CkPa) T (K) p CkPa) 1 (K) p CkPa)

258.74 57.05 312.51 372.51 337.23 704.89 268.07 84.89 317.51 427.07 302.31 793.79 277.90 123.AY 322.46 488.07 3A7.24 888.17 277.91 123.62 322.46 487.61 3A7.25 888. rr6 297.05 241.86 327.56 556.01 352.90 1006.95 307.57 323.78 327.60 556.58 356.97 1098.55 312.09 372.30 332.36 626.83

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119

Vapor pressure of the cure components

Table 4 shows the results of vapor pressure measurements of the pure

components dimethyl ether, methyl chloride. and methanol. The data were

correlated, ~~UWJ the Antoine-Equation

In (pLv/kPa) = A - R / ((T/K)-C) (1)

and the Frost-Kalkwarf-Equation

In (pLv/Torr) = A + B / (T/K) + C ln(T/K) + D (p/Torr) / (T’/K’) (2)

The coefflclents of both equations as well as the standard deviation between

experimental and correlated points are presented Far dimethyl ether, methyl

chloride, and methanol in Table 5.

Vapor-liquid-equilibrium af the system dimethyl ether - methanol

It seemed to be most practical to measure vapor pressures as a Function of

temperature for mixtures of constant composition. Vapor samples were drawn and

analysed at some equilibrium points. It is advantaqous to have lsabaric VI-E-data

in industrial applications and isothermal VLE-data For data reduction. In an

lteratlve procedure isobaric or isothermal data sets were derived From the

experimental equilibrium points.

Due to the inventory of the high volatile companent in the vapor phase and

the effect of samples drawn from the vapor phase, the liquid composition x is

not constant, but varies up to 5.10-’ ,

mol/mol from the total composition zi (see

Table 6).

V x = 2, + - (2, - YJ i ALA (3)

(V/l. = molar vapor-liquid ratlo)

Whenever the vapor composition yi was not determined experimentally, it was

estimated with Raoult in a First approximation and corrected in a second

iteration with calculated vapor compositions resulting from a consistency test.

In a second step corrections were made on the vapor pressures p LW and vapor

composition yi to account for the small deviatlans between the original

experimental liquid composition xi and the defined canstant ki of the isostere.

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120

TABLE 4

Vapor pressure data of dimethyl ether, methyl chloride, and methanol

Dimethyl Ether Methy Chloride T (K) p (kPa) T (K) p (kPa)

Methanol T (K: p (kPa)

253.85 128.07 258.63 155.49 258.64 155.59 261.08 171.07 261.08 171.17 265.41 201.98 268.25 224.34 273.22 267.41 278.00 315.19 287.94 434.55 292.93 506.08 297.60 580.96 302.93 675.74 303.01 677.34 307.57 767.74 312.95 885.28 317.62 997.92 320.40 1069.90 320.51 1072.80

253.81 124.46 254.46 127.88 254.47 127.80 259.24 155.04 259.26 154.99 259.26 155.24 263.12 180.x 264.04 106.77 264.05 186.53 260.79 222.52 272.94 250.35 274.83 275.12 278.90 316.67 202.70 359.80 203.97 374.20 283.97 374.27 288.82 435.98 292.72 091.12 293.94 509.72 298.53 583.11 302.62 654.70 303.44 670.47 307.36 746.76 312.60 858.58 313.28 874.29 318.40 995.93 318.95 1009.81 321.44 1075.36 322.27 1097.91

292.88 12.84 297.75 16.54 302.30 21.18 307.82 27.44 312.81 34.96 317.77 43.70 322.57 54.29 327.75 67.56 332.52 82.54 337.40 lUO.39 342.62 122.90 347.25 146.07 351.24 169.34 356.97 207.19 361.71 243.37

TABLE 5

Coefficients for vapor pressure equations

Substance Equatron A 9 C D U(dP/P)(L>

n-Butane 1) 13.8975 2267.06 28.306 0.0012

2) 52.4421 -4232.12 -5.40579 3.1513 0.0005

Dimethyl Ether 1) 14.2457 2142.93 25.678 0.078

2) 55.2509 -4076.99 -5.84553 2.3335 0.047

Methyl Chloride 1) 14.2817 2166.95 24.680 0.063

2) 47.6175 -3790.56 -4.66670 1.7298 0.049

Methanol 1) 16.6228 3657.61 32.976 0.197

2) 29.2651 -5020.56 -1.32992 -2.9242 0.182

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121

TABLE 6

Experimental VLE data for the system dimethyl ether - methanol

P x Y (kPa) (mol/mol~(mol/mol)

254.36 35.17 0.1229 263.75 50.34 0.1228 272.90 67.54 0.1226 202 .a3 96.44 0.1227 292.78 130.911 0.1227 302.71 175.08 0.1226 312.64 228.82 0.1226 322.65 275.56 0.1226 332.55 376.54 0.1226 342.30 474.07 0.1226 352.15 590.84 0.1227

254.21 70.73 0.4850 0.971 258.57 106.94 0.48Ji 0.789 263.94 131.30 0.4848 0.787 260.56 154.64 0.4837 0.985 273.75 185.32 0.4045 0.983 283.42 253.28 0.4El43 0.776 288.59 295.83 0.11635 0.772 273.41 341.57 0.4EYl 0.968 278.31 391.50 0.4835 0.963 303.41 450.9e 0.4839 0.959 303.46 449.97 0.4830 0.957 308.26 511.30 0.4834 0.953 313.13 580.22 0.4837 0.947 323.49 744.71 0.4835 0.737 333.25 930.61 0.4835 a.921 336.46 lW2.04 0.4834 0.712

254.18 117.62 0.8717 263.50 169.81 0.8719 273.06 240.10 0.8718 282.93 333.70 0.8718 272.77 452.44 0.8717 302.71 602.35 0.8717 312.66 707.16 0.8716 322.73 1014.06 0.8716

253.52 65.21 0.2865 253.54 65.34 II.2868 257.40 81.41 0.2048 263.'90 96.77 0.2862 268.72 114.19 0.2840 273.48 135.07 0.2859 283.4'2 185.09 0.2848 288.56 217.20 0.2857 288.76 217.24 0.2843 278.34 286.13 0.2847 303.50 330.16 0.2854 308.38 374.07 0.2847 313.12 423.16 0.2852 323.27 539.78 0.2887 320.36 608.09 0.2851 338.30 757.10 0.2847 343.12 840.30 0.2851 352.68 1022.70 0.2852

254.23 llO.b3 0.7543 254.94 113.62 0.7544 259.36 134.95 0.7531 263.61 158.30 0.7542 268.28 162.93 0.7540 268.74 191.46 0.7530 273.66 227.93 0.7536 270.36 266.20 0.7528 283.53 315.X 0.7534 280.67 369.33 0.7526 293.54 428.07 0.753ll 298..35 490.78 0.7523 303.57 568.70 0.7526 308.23 643.56 0.7520 313.18 132.74 0.7519 313.39 737.15 0.7521 318.23 831.71 0.7517 323.25 940.19 0.7517 329.06 1077.71 0.7514

0.985 0.965 0.781 0.978 0.975 0.971 0.962 0.756 0.956 0.743 0.935 0.925 0.920 0.884 0.866

0.834

0.991

0.992 0.991 0.989 0.787 0.986 0.983 0.982 0.978 0.975

0.969 0.958

0.948

TABLE 7

Results of the consistency test

Temperature Deviation AADy Deviation AADp (K) (mol/mol) CkPa)

253.15 0.13016 0.011 273.15 0.0038 0.066 323.15 0.0112 0.027

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122

pLvGL) = pLv(x:) + (apLv/aXi)i (X - x:) 1

(4)

Yl$) = Yl(x;) + mpXi), (.Ti - xl) (5)

The derivatives at constant temperature were calculated by using the Van Laar

model for the activity coefficients and the virial equation foe the fugacity

coefficients. The parameters in the Van Laar model were fitted with y taken I from the consistency test.

For inter- and extrapolation, the isosteric vapor pressure data were

correlated by equation (2). The corresponding vapor compositions were correlated

as a function of temperature by

In y1 = A + El / (T/K) + C ln(T/K) (6)

Fig. 4 shows the isosteric vapor pressure curves for the system CZH60-CHJOH.

In Fig. 5 examples of p-x,y diagrams are presented for T = 253, 293 and 323 K

(with data points of Chang et al. 11982) at 293 K). In Fig. 6 examples of T-x,y

diagrams for p = 1, 2 and 5 bars are shown.

/ .

*2l 1 I. I . , , , . 250 260 270 290 310 no 350 370

tomprature T . K

Fig. 4. Vapor pressure of dimethyl ether - methanol mixtures (0 x1=0.000, v x1=o.l227, 0 x1=o.2a54, 0 x1=o.4a39, rxl=0.752a, n x1=0.8718, 0 ~~=~.oooI

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1000

; aw .

5. 600

z i !j 400 4.

200

0 0.0 a.2 0.4 0.6 0.n 1.0

380

360 - -. Y - 340 -

c

- 320 - ,; : : 300 - :

280 -

260 -

240 - 0.0

ccocentr.tion x, l d y, . wl/mol ccmcmtration xl a-d 7, . molfmol cngn m c&u (11 MQi121 c&Y I11

Fig. 5. p-x,y diagram For the system Fig. 6. T-x,y phase diagram the system CH,OCHJ-CH30H at l 253.15 K, r293.15 K, CH,OCH,-CH,OH at l 100 kPa, T 200 kPa, n 323.15 K, v data at 293.15 K measured m 500 kPa, the lines are the results by Chang et al.(lY&?),the lines are the OF Legendre polynomial Fits. results of Legendre polynomial fits

DATA REDUCTION

Thermodynamic consistency test

Whenever T,p,x and y were measured a consistency .test can be and was

performed as recommended by Fredenslund et al. (1977). The excess G'ibbs energy

was represented with a third degree Legendre polynomial. The required Fugacity

coefficients of the vapor phase

P Vi = exp ( ( 2 E Yj Bij - r r Yi Yj Bij 1 - 1

j ij RT (71

were calculated with second virial coefficients 8 estimated by the method of 1J

Hayden and O’Connell (1975).

Table 7 lists the average absolute deviations between experimental and calculated values in vapor composition AADy and in vapor pressure AADp. The

deviations are practically within the experimental inaccuracies.

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124

Models for the excess Gibbs energy

Binary parameters of several popular qE-models were fitted to isothermal

p,x,y-data sets, applying a maximum likelihood method (Prausnitz et al. 19ElO).

The virlal coefficients were estimated as mentioned above. The parameters of the

IJNIQUAC model were fitted for the original model and also for a modified UNIQUAC

model, as suggested by Prausnitz (1980) for alcohols and water.

The resulting parameters and the deviations irl total pressure are listed in

Table 8. The Wilson model and the modified UNIUUAC model can best represent the

set of data.

TABLE E

Results of the parameter estimation

Model Temperature Parameters' 6(q) (K) A 12 A

21 (kPa)

Margules

Van Laar

Wilson

253.15 1.1437 0.2882 1.27 293.15 1.0533 0.2210 3.64 323.15 0.9948 0.1819 6.79

253.15 0.9150 1.5306 0.59 293.15 0.8718 1.3322 1.91 323.15 0.8420 1.2174 4.19

253.15 -647.74 4095.7 0.25 293.15 -789.73 4218.0 0.62 323.15 -929.10 4362.3 1.69

NRTL 253.15 3370.9 -162.90 0.63 293.15 3322.7 -82.258 1.96 323.15 3264.8 0.51182 *.22

UNIQUAC 253.15 2949.2 -511.86 0.37 293.15 2979.5 -533.90 1.28 323.15 2998.8 -542.37 3.16

Mod. UNIOIJAC 253.15 4578.0 -764.42 0.25 293.15 4682. e -871.65 0.61 323.15 4772.2 -945. a2 1.75

l UNIplJAC and NRTL parameters in J/mol Third NRTL parameter a = 0.3

SUMMARY

A phase equilibrium apparatus was designed and built that allows

investigations of VLE and VLLE in a temperature and pressure range interesting

for technical applications.

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125

The vapor pressure curves of dimethyl ether, methyl chloride, methanol, and

n-butane as well as the binary VLE of dimethyl ether - methanol were measured.

Comparison with results of other authors and a consrstency test demonstrated the

reliability of the apparatus and the accuracy of the measurements. The

experimental VLE-data were correlated by several expressions For the excess

Gibbs energy.

Reports on further investrgations on mixtures containing dimethyl ether,

methyl chloride, methanol and water will follow.

ACKNOWLEDGEMENTS

The authors appreciate the Financial support of AIF (Arbeitsgemeinschaft In-

dustrieller Forschunqsverelnigungen e. V. ) for financial support and are very

grateful For the help of the craftsmen in the workshop of our lnstltute.

REFERENCES

Aim, K., 1978. Fluid Phase Equillbrra, 2, 119.

Doublik, T., Fried, V., Hala, E., 19i3. The Vapour Pressures of Pure Substances, Elsevier, Amsterdam.

Chang, E., Calado, J.C.G., Streett, W.E., 1982. J. Chem. Eng. Data, 27, 293.

Fredenslund, A., Gmehllnq, J., Rassmussen, P., 1777. Vapor-Liqurd Cquilibria usrng UNIFAC, Elsevrer, Amsterdam.

Hayden, J.C., O’Connell, J.P., 1975. I.E.C. Proc. Des. Dev. lP, 209.

Haynes, W.M., Goodwrn, R.D., 1982. Thermophysical Properties of Normal Butane from 135 to 700 K at Pressures to 70 MPa. National 8ureau of Standards Monography 169, Washrngton.

Kolbe, 8. and Gmehling, J., 1985. Fluid Phase Equilrbrla, 23, 213.

Kratzke, H., Spillner, C., Muller, S., 1982. J. Chem. Thermodyn., 14, 1175.

Magnus, A., 1836. Ann. Phys. Chem. Poqq., 38. 401.

Pemberton, R-C. and Mash, C.J., 1978. J. Chem. Thermodyn., IO, 867.

Prausnitz, J.M., Anderson, T.F., Grew, E., Eckert, C., Hsieh, R., O’Connell, J.P., 1980. Computer Calculations For Multlcomponent Vapor-Lrquid and Llquid- Liquid Equilibria. Prentice Hall, Englewood Cliffs, N.J..

Rerd, R.C., Prausnltz, J.M., Sherwood, T.K., 1977. Ihe Propertles of Gases and Liquids, McGraw Hill, New York.

Van Ness, H.C. and Gibbs. R.E., 1972. Ind. Eng. Cfiem. Fundam., 11, 3, 010.


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